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Quantum information advantage based on Bell inequalities

Rahul Jain, Srijita Kundu

TL;DR

This paper presents an alternate proposal based on a relation derived from parallel-repeated CHSH games, which has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].

Abstract

Recently, Kretschmer et al. [KGD+25] presented an experimental demonstration of a proposed quantum information advantage protocol. We present an alternate proposal based on a relation derived from parallel-repeated CHSH games. Our memory measure is based on an information measure and is different from [KGD+25], where they count the number of qubits. Our proposal has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].

Quantum information advantage based on Bell inequalities

TL;DR

This paper presents an alternate proposal based on a relation derived from parallel-repeated CHSH games, which has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].

Abstract

Recently, Kretschmer et al. [KGD+25] presented an experimental demonstration of a proposed quantum information advantage protocol. We present an alternate proposal based on a relation derived from parallel-repeated CHSH games. Our memory measure is based on an information measure and is different from [KGD+25], where they count the number of qubits. Our proposal has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].
Paper Structure (12 sections, 5 theorems, 24 equations, 1 figure)

This paper contains 12 sections, 5 theorems, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our proposal
  3. Protocol description.
  4. Noise model.
  5. Concrete parameters.
  6. Comparison with previous work
  7. Preliminaries
  8. Tail bounds
  9. Information measures
  10. Nonlocal games
  11. Task achieving quantum information advantage
  12. Classical lower bound

Key Result

Theorem 1

There exists a $(0, \Omega(n), 0.01)$ noise-robust proof of quantum information advantage. Moreover, this protocol satisfies $\mathsf{I}(X:M) = \mathsf{I}_{\max}^0(X:M)=0$. Let $\delta:=2^{-n/((\ln2)\times 10^4)}$. Any classical prover whose classical memory satisfies will make the verifier accept with probability at most $72\delta^2$.

Figures (1)

  • Figure 1: Circuit implemented by the quantum prover in our proof of quantum information advantage protocol. The unitaries $U^A$ and $U^B$ are Alice and Bob's unitaries in the optimal quantum strategy for the $\mathrm{CHSH}^n$ game. The register $M$ is the quantum memory.

Theorems & Definitions (14)

  • Definition 1: Proof of quantum information advantage
  • Theorem 1
  • Definition 2: Smoothed max-information
  • Definition 3: Classical smoothed spectrum max-information, ABJT18
  • Definition 4
  • Definition 5
  • Theorem 1
  • proof : Proof of Theorem \ref{['thm:main']}
  • Lemma 2
  • proof
  • ...and 4 more